2013/09/20_Pablo Martínez Camblor (University of Oviedo)

On correlated z-values distribution in hypothesis testing

2013/09/20 – 12:00 h | Pablo Martínez Camblor, University of Oviedo

Abstract

In the last decades, multiple-testing problems have received much attention. Different strategies have been considered in order to deal with this problem. The false discovery rate (FDR) is, probably, the most studied criterion. The sequential goodness of fit (SGoF) is one of the most recently proposed approach. Most of the developed procedures are based on the independence among the involved tests, however in general this is a not advisable proviso for a number of practical cases, in spite of this is reasonable in some frameworks. Therefore one of the main problems in order to develop appropriate methods is, precisely, the effect of the dependence among the different tests on the final decisions taken. This paper deals with the consequences of the correlation on the z-values distribution in the general multitesting problem. Some different algorithms are provided in order to approximate the distribution of the expected rejection proportions. The performance of the proposed methods is evaluated from a simulation study in which the Benjamini and Hochberg method to control the FDR, the Lehmann and Romano procedure to control the tail probability of the proportion of false positives (TPPFP) and the Beta-Binomial SGoF procedure are considered as reference. Three different dependence structures are considered. As usual, for a better understanding of the problem, several practical case are also studied.